The Determination On The Number Of Fully Symmetric Function Sets In Partial-Valued Logic

The structure theory of multiple-valued logic functions includes completeness theory, function denotation theory, and unidirectional trapdoor function. One of the most important and fundamental problems is the completeness of function sets. The solution of this problem depends on determining all the precomplete classes in multiple-valued logic function sets.Another important problem in multiple-valued logic completeness theory is the decision and construction for Sheffer function, which reduced to determining the minimal covering of precomplete classes. As to the complete multiple-valued logic function, it was solved. While concerning the partial multiple-valued logic function, it has not been fully solved yet.This thesis mainly discusses the classification of the precomplete set and the decision of the minimal covering in partial k-valued logic, and puts emphasis on studying the fully symmetric relation function sets. First it gives the basic concepts of multiple-valued logic ,introduces the results about the completeness theory in full multiple-valued logic and partial multiple-valued logic, and then, classifies then by similar relation, and lists all precomplete sets which belong to the minimal covering in the fully symmetric relation function sets and the simple separable relation function sets. In the end, it gives the formula of the number of the fully symmetric relation function sets in partial k-valued logic by counting the number of the fully symmetric relation function sets in partial 3,4-valued logic.